Solve -9/25=-4/9x^2

$$- \frac{ 9 }{ 25 } = - \frac{ 4 }{ 9 } { x }^{ 2 }$$

Solve for x

$$x=\frac{9}{10}=0.9$$

$$x=-\frac{9}{10}=-0.9$$

Steps Using Difference of Squares

Multiply both sides by -\frac{9}{4}, the reciprocal of -\frac{4}{9}.

$$-\frac{9}{25}\left(-\frac{9}{4}\right)=x^{2}$$

Multiply -\frac{9}{25} and -\frac{9}{4} to get \frac{81}{100}.

$$\frac{81}{100}=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=\frac{81}{100}$$

Subtract \frac{81}{100} from both sides.

$$x^{2}-\frac{81}{100}=0$$

Multiply both sides by 100.

$$100x^{2}-81=0$$

Consider 100x^{2}-81. Rewrite 100x^{2}-81 as \left(10x\right)^{2}-9^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(10x-9\right)\left(10x+9\right)=0$$

To find equation solutions, solve 10x-9=0 and 10x+9=0.

$$x=\frac{9}{10} x=-\frac{9}{10}$$

Steps by Finding Square Root

Multiply both sides by -\frac{9}{4}, the reciprocal of -\frac{4}{9}.

$$-\frac{9}{25}\left(-\frac{9}{4}\right)=x^{2}$$

Multiply -\frac{9}{25} and -\frac{9}{4} to get \frac{81}{100}.

$$\frac{81}{100}=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=\frac{81}{100}$$

Take the square root of both sides of the equation.

$$x=\frac{9}{10} x=-\frac{9}{10}$$

Steps Using the Quadratic Formula

Multiply both sides by -\frac{9}{4}, the reciprocal of -\frac{4}{9}.

$$-\frac{9}{25}\left(-\frac{9}{4}\right)=x^{2}$$

Multiply -\frac{9}{25} and -\frac{9}{4} to get \frac{81}{100}.

$$\frac{81}{100}=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=\frac{81}{100}$$

Subtract \frac{81}{100} from both sides.

$$x^{2}-\frac{81}{100}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{81}{100} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{81}{100}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{81}{100}\right)}}{2}$$

Multiply -4 times -\frac{81}{100}.

$$x=\frac{0±\sqrt{\frac{81}{25}}}{2}$$

Take the square root of \frac{81}{25}.

$$x=\frac{0±\frac{9}{5}}{2}$$

Now solve the equation x=\frac{0±\frac{9}{5}}{2} when ± is plus.

$$x=\frac{9}{10}$$

Now solve the equation x=\frac{0±\frac{9}{5}}{2} when ± is minus.

$$x=-\frac{9}{10}$$

The equation is now solved.

$$x=\frac{9}{10} x=-\frac{9}{10}$$